Mean-field limit of a hybrid system for multi-lane multi-class traffic

2020/07/29 by Gong, Xiaoqian, Piccoli, Benedetto, Visconti, Giuseppe · 1 citation
#34A38 #35Q83 #90B20 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Optimization and Control (math.OC) #Physics and Society (physics.soc-ph)

paper · doi:10.48550/arxiv.2007.14655

Abstract

This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with the autonomous vehicles possibly influenced by external policy makers. First a finite-dimensional hybrid system is developed based on the continuous Bando-Follow-the-Leader dynamics coupled with discrete events due to lane-change maneuvers. Then the mean-field limit of the finite-dimensional hybrid system is rigorously derived for the dynamics of the human-driven vehicles. The microscopic lane-change maneuvers of the human-driven vehicles generates a source term to the mean-field PDE. This leads to an infinite-dimensional hybrid system, which is described by coupled Vlasov-type PDE, ODEs and discrete events.

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